A man buys shares of face value Rs. 25 each in a company that pays a 9% dividend. If his investment is such that it yields 10% on the money he puts in, at what price per share did he buy the shares?

Introduction / Context:
This problem asks for the purchase price of a share, given its face value, the declared dividend rate on face value, and the effective yield that the investor actually earns on his investment. It illustrates how the purchase price affects the relationship between the nominal dividend rate and the actual return on the investor's money.

Given Data / Assumptions:

• Face value of each share = Rs. 25.
• Dividend rate = 9% on face value.
• Yield on the investor's money = 10%.
• We must find the market price P at which the shares are purchased.
• No brokerage is mentioned.

Concept / Approach:
First compute the annual dividend per share using the face value and dividend rate. Then apply the yield formula to find the purchase price. Yield on investment is defined as:
yield % = (annual dividend per share / purchase price per share) * 100 We set this yield equal to 10% and solve for the unknown purchase price P.

Step-by-Step Solution:
Step 1: Face value of the share = Rs. 25. Step 2: Dividend rate = 9%. Step 3: Annual dividend per share = 9% of 25 = (9 / 100) * 25 = Rs. 2.25. Step 4: Let P be the purchase price per share. Step 5: Yield on investment is 10%, so (2.25 / P) * 100 = 10. Step 6: Simplify: 2.25 / P = 10 / 100 = 0.10. Step 7: Solve for P: P = 2.25 / 0.10 = Rs. 22.50. Step 8: Therefore, the man bought the shares at Rs. 22.50 each.

Verification / Alternative check:
Check the yield explicitly: if the share costs Rs. 22.50 and pays a dividend of Rs. 2.25 per year, then yield % = (2.25 / 22.50) * 100 = 0.10 * 100 = 10%. This matches the given yield, confirming that Rs. 22.50 is the correct purchase price.

Why Other Options Are Wrong:
At Rs. 22, the yield would be (2.25 / 22) * 100, which is slightly above 10%. At Rs. 20.45, the yield is even higher. At Rs. 12.50, the yield would be extremely high, far more than 10%. Purchasing at Rs. 25 (face value) would produce a yield of only (2.25 / 25) * 100 = 9%, equal to the dividend rate but less than the desired 10%. Only Rs. 22.50 produces the exact 10% return.

Common Pitfalls:
Some students mistakenly treat 9% as the yield and ignore the 10% figure, or they try to average the two percentages. Others forget to divide dividend by price when calculating yield and instead subtract percentages. Always use the yield formula with the correct base: yield depends on the purchase price, not on the face value.

Final Answer:
He bought the shares at a price of Rs. 22.50 per share.